F2(Cn)空间上无界的复对称加权复合算子
Unbounded Complex Symmetric Weighted Composition Operators on F2(Cn) Space
DOI: 10.12677/PM.2021.118168, PDF,    国家自然科学基金支持
作者: 黄周萍：华南农业大学，广东 广州
关键词: F2(Cn)空间；复对称性；加权复合算子；自伴性；F2(Cn) Space； Complex Symmetry； Weighted Complex Operator； Self Adjoint
摘要: 本文研究了n维Fock空间上加权复合算子TψDθkf:=ψ⋅f(k)。θ关于共轭(Jf)(z)=(C1,0,c)f(z)=cf(z)的复对称性和自伴性，其中θ和ψ是Cn上的两个整函数，k是非负整数，得出了算子TψDθk是J-自伴的等价刻画。此外，我们还给出了TψDθk是厄米特算子的充要条件。
Abstract: In this paper, we study the complex symmetry and self-adjoint of the conjugate (Jf)(z)=(C1,0,c)f(z)=cf(z) by the weighted complex operator TψDθkf:=ψ⋅f(k)。θ on n dimensional Fock space, where θ and ψ are two entire functions, k is a nonnegative integer. We give an equivalence characterization where the operator TψDθk is a J-self-adjoint. In addition, we prove that the unbounded maximal weighted composition operator is self-adjoint.
文章引用：黄周萍. F2(Cn)空间上无界的复对称加权复合算子[J]. 理论数学, 2021, 11(8): 1493-1504. https://doi.org/10.12677/PM.2021.118168

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